Download Lesson 23 – 2.1 Trig Ratios with Acute Angles.PPT

PRIMARY TRIGONOMETRIC RATIOS
𝒔𝑖𝑛𝜃 =
𝒐𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝒉𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝐴
𝒄𝑜𝑠𝜃 =
𝒂𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝒉𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝒕𝑎𝑛𝜃 =
SOH-CAH-TOA
hypotenuse
opposite
𝜃
𝐵
adjacent
𝐶
𝒐𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝒂𝑑𝑗𝑎𝑐𝑒𝑛𝑡
 Determine
the sine, cosine and tangent of
angle 𝜃 𝑖𝑛 ∆𝐴𝐵𝐶.
CALCULATIONS
SOH-CAH-TOA
𝐵
26 units
10 units
𝜃
𝐶
24 units
𝐴
 Determine
the sine, cosine, and tangent of
angle Q in ∆𝑃𝑄𝑅 to three decimal places.
𝑄
𝑃
4.2 𝑚
3.3 𝑚
𝑅
Pablo has a well behind his cottage. To measure its
depth, he measures the diameter of the well and
the angle of depression. Determine the depth of
Pablo’s well to the nearest foot.
6ft
72o
d=?
6ft
Susan is building a skateboard ramp. She wants it
to have a vertical rise of 50cm over a horizontal
distance of 1.0m. At what angle of elevation
should she build the ramp the nearest degree?
50 cm
𝜃
1.0 m
∆𝑇𝑈𝑉 is a right triangle, such that angle U = 90o,
u = 5.4m, and v = 3.2m. Solve ∆𝑇𝑈𝑉.
“SOLVE” = Find all unknowns
𝑇
5.4 m
3.2 m
𝜃
𝑈
𝑉
p. 80 #1-7, 9, 10a, 11, 13ab